On the Output of a GI/M/N Queuing System with Interrupted Poisson Input

We consider the output process of a GI/M/N queuing system with interrupted Poisson input. The interrupted Poisson input is frequently used to characterize alternate routed traffic and may be shown to be equivalent to a mixture of two exponential distributions. We characterize the departure process as a semi-Markov process and give results for the joint distribution of the number of customers in the system and the state of the input process at service completions. We also present results relating to the interdeparture time distribution and the distribution of the nonbusy period and compare the results with some known results for single-server systems.